We also define addition and multiplication for arbitrary numbers of cardinals.
Suppose I is an index set and κi is a cardinal for every i∈I.
Then ∑i∈Iκi is defined to be
the cardinality of the union ⋃i∈IAi,
where the Ai are pairwise disjoint and |Ai|=κi for each i∈I.
Similarly, ∏i∈Iκi is defined to be the cardinality of the
Cartesian product (http://planetmath.org/GeneralizedCartesianProduct)
∏i∈IBi, where |Bi|=κi for each i∈I.